How do you factor the expression #n^2 - 28n + 196#?

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Answer 1 · 2016-03-05T16:52:56

#color(blue)( (n-14) (n-14) # is the factorised form of the expression.

#n^2-28n+196#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #an^2 + bn + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*196 = 196#

AND

#N_1 +N_2 = b = -28#

After trying out a few numbers we get #N_1 = -14# and #N_2 =-14#

#-14*-14 = 196#, and #(-14)+(-14)= -28#

#n^2-28n+196 = n^2-14n - 14n+196#

# = n (n-14) -14(n-14)#

#color(blue)( (n-14) (n-14) # is the factorised form of the expression.